Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
Superfast Multifrontal Method for Large Structured Linear Systems of Equations - MaRDI portal

Superfast Multifrontal Method for Large Structured Linear Systems of Equations

From MaRDI portal
Publication:3584165

DOI10.1137/09074543XzbMath1195.65031MaRDI QIDQ3584165

Jian-Lin Xia, Xiaoye Sherry Li, Ming Gu, Shivkumar Chandrasekaran

Publication date: 19 August 2010

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)




Related Items (89)

A multilevel approach for trace system in HDG discretizationsL-sweeps: a scalable, parallel preconditioner for the high-frequency Helmholtz equationSuperDC: Superfast Divide-And-Conquer Eigenvalue Decomposition With Improved Stability for Rank-Structured MatricesA Direct Elliptic Solver Based on Hierarchically Low-Rank Schur ComplementsTrace transfer-based diagonal sweeping domain decomposition method for the Helmholtz equation: algorithms and convergence analysisSweeping preconditioner for the Helmholtz equation: Hierarchical matrix representationExistence of $\mathcal {H}$-matrix approximants to the inverses of BEM matrices: The simple-layer operatorLinear-scaling selected inversion based on hierarchical interpolative factorization for self Green's function for modified Poisson-Boltzmann equation in two dimensionsA fast block low-rank dense solver with applications to finite-element matricesMultigrid-based `shifted-Laplacian' preconditioning for the time-harmonic elastic wave equationFast Algorithms for High Frequency Wave PropagationA new multilevel method for electrostatic problems through hierarchical loop basisAn efficient, memory-saving approach for the Loewner frameworkHierarchical orthogonal factorization: sparse least squares problemsFast Structured Direct Spectral Methods for Differential Equations with Variable Coefficients, I. The One-Dimensional CaseHierarchical Interpolative Factorization for Elliptic Operators: Differential EquationsA fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matricesA fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensionsEfficient preconditioning of \(hp\)-FEM matrices by hierarchical low-rank approximationsNested Domain Decomposition with Polarized Traces for the 2D Helmholtz EquationA fast direct solver for two dimensional quasi-periodic multilayered media scattering problemsAcoustic inverse scattering via Helmholtz operator factorization and optimizationDistributed-memory hierarchical interpolative factorizationFast and accurate numerical methods for solving elliptic difference equations defined on latticesFast Sparse Selected InversionA convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equationsEfficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updatesLow-Rank Correction Methods for Algebraic Domain Decomposition PreconditionersA fast direct solver for a class of elliptic partial differential equationsA direct solver for variable coefficient elliptic PDEs discretized via a composite spectral collocation methodA Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct SolutionsOn the Complexity of the Block Low-Rank Multifrontal FactorizationA fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite‐element matricesFMM-LU: A Fast Direct Solver for Multiscale Boundary Integral Equations in Three DimensionsAn \(O(N)\) algorithm for constructing the solution operator to 2D elliptic boundary value problems in the absence of body loadsSimple non-extensive sparsification of the hierarchical matricesSecond‐order accurate hierarchical approximate factorizations for solving sparse linear systemshm-toolbox: MATLAB Software for HODLR and HSS MatricesRandomized preprocessing versus pivotingMulti-core parallel robust structured multifrontal factorization method for large discretized PDEs\(\mathcal {H}\)-matrix approximability of the inverses of FEM matricesFast Factorization Update for General Elliptic Equations Under Multiple Coefficient UpdatesA fast direct solver for elliptic problems on general meshes in 2DAn Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank ApproximationsAn Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three DimensionsAn Adaptive High Order Direct Solution Technique for Elliptic Boundary Value ProblemsBridging the Gap Between Flat and Hierarchical Low-Rank Matrix Formats: The Multilevel Block Low-Rank FormatHierarchical interpolative factorization preconditioner for parabolic equationsHigh scalable non-overlapping domain decomposition method using a direct method for finite element analysisFast algorithms for large dense matrices with applications to biofluidsFast structured LU factorization for nonsymmetric matricesAn \(O(N \log N)\) hierarchical random compression method for kernel matrices by sampling partial matrix entriesA survey on direct solvers for Galerkin methodsAn Enriched Multiscale Mortar Space for High Contrast Flow ProblemsA Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz EquationA direct solver with \(O(N)\) complexity for integral equations on one-dimensional domainsA Recursive Skeletonization Factorization Based on Strong AdmissibilityA parallel shared-memory implementation of a high-order accurate solution technique for variable coefficient Helmholtz problemsThe Inverse Fast Multipole Method: Using a Fast Approximate Direct Solver as a Preconditioner for Dense Linear SystemsAn algebraic multifrontal preconditioner that exploits the low‐rank propertyCompressing Rank-Structured Matrices via Randomized SamplingAn improved divide-and-conquer algorithm for the banded matrices with narrow bandwidthsA survey of direct methods for sparse linear systemsFast construction of hierarchical matrix representation from matrix-vector multiplicationA spectrally accurate direct solution technique for frequency-domain scattering problems with variable mediaParallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficientsAn Algebraic Multilevel Preconditioner with Low-Rank Corrections for Sparse Symmetric MatricesThe method of polarized traces for the 2D Helmholtz equationPreconditioners for hierarchical matrices based on their extended sparse formAn \(O(N)\) direct solver for integral equations on the planeA direct solver for elliptic PDEs in three dimensions based on hierarchical merging of Poincaré-Steklov operatorsHierarchical Interpolative Factorization for Elliptic Operators: Integral Equations\({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional LaplacianRandomized linear algebra for model reduction. I. Galerkin methods and error estimationA Fast Algorithm for Simulating Multiphase Flows Through Periodic Geometries of Arbitrary ShapeEfficient preconditioning of \(h p\)-FEM matrix sequences with slowly-varying coefficients: an application to topology optimizationFast Alternating BiDirectional Preconditioner for the 2D High-Frequency Lippmann--Schwinger EquationParallel Randomized and Matrix-Free Direct Solvers for Large Structured Dense Linear SystemsA Power Schur Complement Low-Rank Correction Preconditioner for General Sparse Linear SystemsRobust and Accurate Stopping Criteria for Adaptive Randomized Sampling in Matrix-Free Hierarchically Semiseparable ConstructionVariational training of neural network approximations of solution maps for physical modelsSubspace Iteration Randomization and Singular Value ProblemsBridging and Improving Theoretical and Computational Electrical Impedance Tomography via Data CompletionA high-order accurate accelerated direct solver for acoustic scattering from surfacesInterconnected hierarchical structures for fast direct elliptic solutionA Parallel Geometric Multifrontal Solver Using Hierarchically Semiseparable StructureA Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using RandomizationA Hierarchical Preconditioner for Wave Problems in Quasilinear ComplexityHierarchical Orthogonal Factorization: Sparse Square Matrices




This page was built for publication: Superfast Multifrontal Method for Large Structured Linear Systems of Equations